feat(logo): single-tone export, Bélo-weight unified stroke, tuned seed

[debuggingfuture]

Three changes to the exported logo/favicon mark: overlapping lines no longer darken, every export renders at one consistent stroke weight — set to the Airbnb Bélo's line-to-height ratio — and the seed is tuned to 0.363 + 0.965i.

Problem & Insight

scripts/export-logo.mjs had two independent inconsistencies:

1. Overlap darkening. The unit box and the F polyline were drawn as two separate translucent strokes (box α 0.4 under polyline α 0.55). Canvas composites each stroke() independently, so where the polyline crossed the box the layers stacked (~0.73 alpha) and read as a denser square.
2. Stroke weight split. The 766 logo used a fixed 5.2px stroke (0.68% of the image) while favicons scaled at 3.5% — so the mark looked much finer as the full logo than as a tab/home-screen icon.

For the target weight we measured the Airbnb Bélo from the official SVG (viewBox 320.1×99.9): its uniform line is 7.023 units against the symbol's 99.9-unit height — ≈7.03% of the mark's height. Our box spans the image edge to edge, so the image size is the mark height and that ratio carries over directly.

Take

• Single mint tone, single path. Box + F are now one path stroked once in one alpha. A lone stroke() unions its own coverage, so overlaps stay that flat color rather than compositing into a darker patch — holds for both the dark-bg and transparent variants.
• One stroke-to-image ratio everywhere, at Bélo weight: STROKE_RATIO = 7.023/99.9 ≈ 0.0703 — ≈54px on the 766 logo, 12.7px on the 180px apple-touch, 4.5px on the 64px favicon. The 2px floor remains as a safety net but is no longer hit at any exported size.
• One ink alpha (0.85) for every export. The full logo was previously α 0.55 — much dimmer than the favicons, so on the dark background it read as faint/near-transparent. Everything now uses the favicon/apple-touch brightness (mint 176,222,240 at 0.85 over #0a0a0a).
• Seed tuned to 0.363 + 0.965i. A nudge off the exact 3:41 Numberphile value (0.362 + 0.953i) for a cleaner F.

The rendering still diverges from the live /f page on purpose (the page keeps its two-tone layering and thinner proportional strokes); documented in LOGO.md. The seed is now synced — the /f page uses 0.363 + 0.965i too, with its copy/readout updated and an honest pointer to the original 3:41 value it's nudged off.

Verification

• Bélo reference measured by run-length histogram over the rendered official SVG (10k+ scanline runs): mode 7.02 viewBox units on the 92.8×99.9 symbol → 7.03% of height.
• Rendered box-edge stroke measured per asset at half-ink threshold: 766 → 54px (7.05%), 180 → 13px (7.22%), 64 → 4px (6.25%, antialias rounding of the drawn 4.5px). All within a pixel of the drawn size × 0.0703.
• Transparent PNG pixel-probe: max alpha 217 (= 0.85·255) across the whole image, zero pixels above it → no overlap accumulates.

Key actions

• Single-tone single-path stroke (no overlap darkening)
• Unified stroke-to-image ratio across logo + favicons, matched to the Airbnb Bélo
• Seed tuned to 0.363 + 0.965i
• Re-exported all four assets (logo_f_box.png, logo_f_box_transparent.png, favicon.png, apple-touch-icon.png)
• LOGO.md updated
• Synced /f page seed + copy to match the logo